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Stat Methods Med Res. 2016 Aug;25(4):1359-80. doi: 10.1177/0962280213481053. Epub 2013 Apr 16.

Linear combination methods to improve diagnostic/prognostic accuracy on future observations.

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Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, MD, USA.
Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD, USA.
Department of Biostatistics, State University of New York at Buffalo, Buffalo, NY, USA


Multiple diagnostic tests or biomarkers can be combined to improve diagnostic accuracy. The problem of finding the optimal linear combinations of biomarkers to maximise the area under the receiver operating characteristic curve has been extensively addressed in the literature. The purpose of this article is threefold: (1) to provide an extensive review of the existing methods for biomarker combination; (2) to propose a new combination method, namely, the nonparametric stepwise approach; (3) to use leave-one-pair-out cross-validation method, instead of re-substitution method, which is overoptimistic and hence might lead to wrong conclusion, to empirically evaluate and compare the performance of different linear combination methods in yielding the largest area under receiver operating characteristic curve. A data set of Duchenne muscular dystrophy was analysed to illustrate the applications of the discussed combination methods.


Multiple biomarkers; area under the receiver operating characteristic curve; diagnostic/prognostic accuracy; linear combination; receiver operating characteristic curve

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